(y-5)(7y+9)=0

Solution for (y-5)(7y+9)=0 equation:

(y-5)(7y+9)=0

We multiply parentheses ..

(+7y^2+9y-35y-45)=0

We get rid of parentheses

7y^2+9y-35y-45=0

We add all the numbers together, and all the variables

7y^2-26y-45=0

a = 7; b = -26; c = -45;
Δ = b2-4ac
Δ = -262-4·7·(-45)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-44}{2*7}=\frac{-18}{14}
=-1+2/7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+44}{2*7}=\frac{70}{14}
=5
$